Concept of Rate

Before defining rate, first we consider some examples.

1. If one dozen eggs cost 24 Rs., what is the cost of 1 egg?

(Ans). One dozen eggs costs = 24 Rs
Cost of 1 egg = 24/12=2Rs/egg

2. A car travels 540 km and consumes 60 liters petrol. Find the distance traveled in liters.

(Ans). With 60 liters, distance travelled= 540km
With 1 liter, distance travelled = 540/60=9km/liter

3. A boy works for 5 hours and is paid 120 Rs. Find his pay for one hour.

(Ans) In 5 hours boy gets = 120 Rs.
In 1 hour boy gets = 120/5=24Rs/hour

In each of the above examples, the two quantities that are the quantity in the numerator and the quantity in the denominator have different units. Conversely, in a ratio both quantities have the same units.

The division of two quantities having different units is called RATE.
In the above examples, we have

  1. Rate = 24/12 = 2Rs/egg
  2. Rate = 540/60 = 9km/liter
  3. Rate = 120/5 = 24Rs/hour

Example:
A car uses 40 liters of petrol to travel 320 km. How far can it travel with 32 liters?

Solution:
With 40 liters the car traveled = 320km
With 1 liter the car traveled = 320/40 = 6km/liter
With 32 liter the car traveled = (8km/liter)(32liter) = 256km